{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm, logistic\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 为在Matplotlib中显示中文，设置特殊字体\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']\n",
    "# 正确显示负号\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "plt.rcParams.update({'font.size': 13})\n",
    "# 创建一个图形框，在里面只画一幅图\n",
    "fig = plt.figure(figsize=(9, 6), dpi=100)\n",
    "ax = fig.add_subplot(111)\n",
    "x = np.linspace(-8, 4, 100)\n",
    "alpha = 1.702\n",
    "normal = norm.cdf(x)\n",
    "logit = logistic.cdf(alpha * x)\n",
    "ax.plot(x, normal,\n",
    "        label='标准正态分布：'\n",
    "            + r'$F(x) = \\int_{-\\infty}^{x}\\frac{1}{\\sqrt{2\\pi}}{\\rm e}^{-\\frac{t^{2}}{2}}$'\n",
    "            + r'${\\rm d}t$')\n",
    "ax.plot(x, logit, 'k-.',\n",
    "        label=r'最佳近似的逻辑分布：$F(x) = \\frac{1}{1 + {\\rm e}^{-1.702x}}$')\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('累积分布函数：$F(x)$')\n",
    "legend = plt.legend(shadow=True, fontsize=16)\n",
    "plt.savefig('normal_logit_approx.png', dpi=200)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
